The one-loop divergences were calculated in other models of QG,
including fourth-derivative QG with the action (REF ) and
the polynomial superrenormalizable model (REF ). The case
of the theory (REF ) is treated in full detail in another
Chapter of this Section of our Handbook and we will not discuss
the technical details here. From the general perspective, this
calculation was relevant for several reasons. There is a growing
understanding that the construction of QG which is not restricted
to the low-energy domain, cannot be successful without higher
derivative and the same is true in the semiclassical theory. Then,
one of the “traditional” expectations is to advance in the problem
of ghosts and instabilities by exploring quantum corrections and,
at the first place, the logarithmic contributions
[1]}, [2]}. As we already know, these contributions
are directly related to the UV divergences
